Acceleration of the universe in the Einstein frame of a metric-affine f(R) gravity

We show that inflation and current cosmic acceleration can be generated by a metric-affine f® gravity formulated in the Einstein conformal frame, if the gravitational Lagrangian L® contains both positive and negative powers of the curvature scalar R. In this frame, we give the equations for the expansion of the homogeneous and isotropic matter-dominated universe in the case L®=R+{R^3}/{\beta^2}-{\alpha^2}/{3R}, where \alpha and \beta are constants. We also show that gravitational effects of matter in such a universe at very late stages of its expansion are weakened by a factor that tends to 3/4, and the energy density of matter \epsilon scales the same way as in the \Lambda-CDM model only when \kappa*\epsilon<<\alpha.